Biomedical subjects

Gérard Tayeb

Publications and source records attributed to Gérard Tayeb.

7 recordsLinked to original sources

PubMed2004

Enhanced transmission due to nonplasmon resonances in one- and two-dimensional gratings.

Enhanced transmission through subwavelength slit gratings and hole arrays is studied in view of its application in the far-infrared and microwave domains. Because for perfectly conducting gratings, plasmon resonances are not expected to produce an enhanced transmission, other kinds of resonance, such as Fabry-Perot, waveguide-mode, and cavity-mode resonances, are studied. The possibility of reaching 100% transmittivity for some particular wavelengths is established when two superimposed identical gratings are used while each of them transmits approximately 1% off resonance. A similar transmission is obtained with hole arrays. The study of the field map inside the groove region allows our establishing the nature of the resonance, that is involved. Comparison of the bandwidth with respect to the wavelength or incidence given by various kinds of resonance is presented.

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PubMed2004

Combined fictitious-sources-scattering-matrix method.

We describe a way to combine the method of fictitious sources and the scattering-matrix method. The resulting method presents concurrently the advantages of these two rigorous methods. It is able to solve efficiently electromagnetic problems in which the structure is made up of a jacket containing an arbitrary set of scatterers. The method is described in a two-dimensional case, but the basic ideas could be easily extended to three-dimensional cases.

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PubMed2004

Diffraction theory in TM polarization: application of the fast Fourier factorization method to cylindrical devices with arbitrary cross section.

The diffraction of an electromagnetic wave by a cylindrical object with arbitrary cross section is studied by taking advantage of recent progress in grating theories. The fast Fourier factorization method previously developed in Cartesian coordinates is extended to cylindrical coordinates thanks to the periodicity of both the diffracting object and the incident wave with respect to the polar angle theta. Thus Maxwell equations in a truncated Fourier space are derived and separated in TE and TM polarization cases. The new set of equations for TM polarization is resolved numerically with the S-matrix propagation algorithm. Examples of elliptic cross sections and cross sections including couples of nonconcentric circles show fast convergence of the results, for both dielectric and metallic materials, as well as good agreement with previous published results. Thus the method is suitable for an extension to conical (out-of-plane) diffraction, which will allow studying mode propagation along microstructured fibers.

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PubMed2003

Theoretical study of photonic band gaps in woodpile crystals.

We investigate numerically the existence of photonic band gaps in woodpile crystals. We present a numerical method specifically developed to solve Maxwell's equations in such photonic structures. It is based upon a rigorous mathematical formulation and leads to a considerable improvement of the convergence speed as compared to other existing numerical methods. We tested our method by comparing the calculated reflectivity with measurements on an actual sample, i.e., a silicon woodpile photonic crystal designed for 1.5 microm wavelength. Excellent agreement is obtained, provided the main structural imperfections of the sample are taken into account. We show that the existence of photonic band gaps in woodpile crystals requires an index contrast higher than 2.05 +/- 0.01. The effects of imperfections of such structures with an index contrast equal to 2.25 are also investigated. Thus, the relative band gap width falls from 3.5% to 2.2% with structurals imperfection similar to those of the sample.

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PubMed2002

A metamaterial for directive emission.

In this paper we present the first results on emission in metamaterial. We show how the specific properties of metallic composite material can modify the emission of an embedded source. We show that under proper conditions the energy radiated by a source embedded in a slab of metamaterial will be concentrated in a narrow cone in the surrounding media. An experimental demonstration of this effect is given in the microwave domain, and the constructed antenna has a directivity equivalent to the best reported results with photonic-crystal-based antennas but using a completely different physical principle [B. Temelkuaran, J. Appl. Phys. 87, 603 (2000)]].

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PubMed2002

Staircase approximation validity for arbitrary-shaped gratings.

An electromagnetic study of the staircase approximation of arbitrary shaped gratings is conducted with three different grating theories. Numerical results on a deep aluminum sinusoidal grating show that the staircase approximation introduces sharp maxima in the local field map close to the edges of the profile. These maxima are especially pronounced in TM polarization and do not exist with the original sinusoidal profile. Their existence is not an algorithmic artifact, since they are found with different grating theories and numerical implementations. Since the number of the maxima increases with the number of the slices, a greater number of Fourier components is required to correctly represent the electromagnetic field, and thus a worsening of the convergence rate is observed. The study of the local field map provides an understanding of why methods that do not use the staircase approximation (e.g., the differential theory) converge faster than methods that use it. As a consequence, a 1% accuracy in the efficiencies of a deep sinusoidal metallic grating is obtained 30 times faster when the differential theory is used in comparison with the use of the rigorous coupled-wave theory. A theoretical analysis is proposed in the limit when the number of slices tends to infinity, which shows that even in that case the staircase approximation is not well suited to describe the real profile.

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PubMed2002

From scattering or impedance matrices to Bloch modes of photonic crystals.

The dispersion relation of Bloch waves is derived from the properties of a single grating layer. A straightforward way to impose the Bloch condition leads to the calculation of the eigenvalues of the transfer matrix through the single grating layer. Unfortunately, the transfer-matrix algorithm is known to be unstable as a result of the growing evanescent waves. This problem appears again in the calculation of the eigenvalues, making unusable the transfer matrix in numerous practical problems. We propose two different algorithms to circumvent this problem. The first one takes advantage of scattering matrices, while the second one takes advantage of impedance matrices. Numerical evidence of the efficiency of the algorithms is given. Dispersion diagrams of simple cubic and woodpile photonic crystals are obtained by using, respectively, the scattering and impedance matrices.

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